In this project, a fourth order finite difference method is presented for solving third order linear two point boundary value problems. We use grid points to derive this method. The present method is convergent to fourth order accuracy. In addition, we show that this method is unconditionally stable. A MATLAB code is developed for the finite difference method to obtain the numerical results. Three numerical examples are considered to illustrate the efficiency of the present method. The numerical results, maximum absolute error and rate of convergence are tabulated and compared with the exact solution. Graphs are also depicted in support of the numerical results. From the results, we have observed that the present method approximates the exact solution very well.